Which of the following languages can be recognized by Non-Deterministic Finite Automata (NFA) but cannot be recognized by Deterministic Finite Automata (DFA)?
A. $$L_1 =$$​ {w $$\in$$​ {0, 1} *| the length of w is even}
B. $$L_2 =$$​ {w $$\in$$​ {0, 1} *| the length of w is odd}
C. $$L_3 =$$​ {w $$\in$$​ {0, 1} *| all 0's come before all 1's in w}
D. $$L_4 =$$​ {w $$\in$$​ {0, 1} *| w contains an equal number of 0's and 1's}
E. $$L_5 =$$​ {w $$\in$$​ {0, 1} *| all 1's come before all 0's in w}
Choose the correct answer from the options given below:

Correct option is D

1. Analyzing Each Language:
· $$L_1$$​ and $$L_2$$​ (Length Constraints): These languages are regular languages. DFA and NFA can both recognize languages based on the even or odd length of strings.
· $$L_3$$​ (0’s before 1’s): This is also a regular language as it enforces a simple ordering that DFAs can handle.
· $$L_4$$​ (Equal 0’s and 1’s): This language is non-regular because it requires counting and matching the number of 0’s and 1’s, which NFAs can handle but DFAs cannot.
· $$L_5$$​ (1’s before 0’s): This language is non-regular because it enforces a specific order and requires memory of the transition from 1’s to 0’s, which NFAs can handle but DFAs cannot.
2. Conclusion:
· Only $$L_4$$​ and $$L_5$$​ require capabilities beyond what DFAs can handle, so they can be recognized by an NFA but not by a DFA.
Information Booster:
· DFA vs. NFA:
· DFA (Deterministic Finite Automata): Can recognize regular languages but cannot handle certain complex counting requirements.
· NFA (Non-Deterministic Finite Automata): Has more flexibility in state transitions, which allows it to recognize some languages that require memory or counting.
Additional Knowledge:
· $$L_3$$​ can be recognized by both DFA and NFA since it only requires a regular structure.
· $$L_4$$​ and $$L_5$$​ are context-sensitive and require more memory than DFAs can provide.